The **Bond Duration Calculator** can be used to derive the duration of a bond:

Semiannually

Quarterly

Monthly

## Example of using the Bond Duration Calculator

Suppose that you have a bond, where the:

- Number of years to maturity is
**2** - Yield is
**8%** - Bond face value is
**1000** - Annual coupon rate is
**6%** - Payments are
**semiannual**

(1) What is the bond’s Macaulay Duration?

(2) What is the bond’s Modified Duration?

You can easily calculate the bond duration using the *Bond Duration Calculator*. Simply enter the following values in the calculator:

Once you are done entering the values, click on the 'Calculate Bond Duration' button and you'll get the Macaulay Duration of **1.912 **and the Modified Duration of **1.839**:

## Formulas to Calculate the Bond Duration

You can use the following formula to calculate the **Macaulay Duration (MacD)**:

(t1*FV)(C) (tn*FV)(C) (tn*FV) MacD = (m*PV)(1+YTM/m)^{mt1}+ ... + (m*PV)(1+YTM/m)^{mtn}+ (PV)(1+YTM/m)^{mtn }

Where:

**m**= Number of payments per period**YTM**= Yield to Maturity**PV**= Bond price**FV**= Bond face value**C**= Coupon rate**t**= Time in years associated with each coupon payment_{i}

For example, let's suppose that you have a bond, where the:

- Number of years to maturity is 2
- Yield is 8%
- Bond face value is 1000
- Annual coupon rate is 6%
- Payments are semiannual
- Bond price is 963.7

Based on the above information, here are all the components needed in order to calculate the Macaulay Duration:

**m**= Number of payments per period =**2****YTM**= Yield to Maturity = 8% or**0.08****PV**= Bond price =**963.7****FV**= Bond face value =**1000****C**= Coupon rate = 6% or**0.06**

Additionally, since the bond matures in 2 years, then for a semiannual bond, you'll have a total of 4 coupon payments (one payment every 6 months), such that:

**t**= 0.5 years_{1 }**t**= 1 years_{2 }**t**= 1.5 years_{3 }**t**=_{4}**t**= 2 years_{n}

Pay special attention to the *last period* (**t _{4}**=

**t**= 2 years) which requires both the coupon payment

_{n}*as well as*the final principal repayment.

Let's now plug all those components within the MacD formula:

(0.5*1000)(0.06) (1*1000)(0.06) (1.5*1000)(0.06) (2*1000)(0.06) (2*1000) MacD = (2*963.7)(1+0.08/2)^{2*0.5}+ (2*963.7)(1+0.08/2)^{2*1}+ (2*963.7)(1+0.08/2)^{2*1.5}+ (2*963.7)(1+0.08/2)^{2*2}+ (963.7)(1+0.08/2)^{2*2}

MacD = 0.01496 + 0.02878 + 0.04151 + 0.05322 + 1.7740 = **1.912**

Once you calculated the Macaulay duration, you'll be able to use the formula below in order to derive the **Modified Duration (ModD)**:

MacD ModD = (1+YTM/m)

For our example:

1.9124 ModD = (1+0.08/2)

The Modified duration is therefore = **1.839**

You may refer to the following guide that further explains how to calculate the Bond Duration.